Suppose a coin is dropped from the top of the Empire State Building in New York, which

is 1,454 feet tall. The position function for free-falling objects is: s(t) = -16t² + v₀t + s_0,

where v0 is the initial velocity and s0 is the initial position. Show all work and explain why its correct.

A. Determine the position and velocity functions for the coin.

B. Determine the average velocity of the coin on the interval [1, 3].

C. Find the instantaneous velocities when t = 1 and t = 3.

D. At what time is the instantaneous velocity of the coin equal to the average velocity of the coin found in Part B?

E. What is the name of the theorem that says there must be at least one solution to Part D?

F. Find the velocity of the coin just before it hits the ground